AtCoder题解｜ABC 123D Cake 123

题目信息 📚

【题目描述】

The Patisserie AtCoder sells cakes with number-shaped candles. There are $X$, $Y$, and $Z$ kinds of cakes with 1-shaped, 2-shaped, and 3-shaped candles, respectively. Each cake has an integer value called deliciousness, as follows:

The deliciousness of the cakes with 1-shaped candles are $A_1, A_2, \ldots, A_X$.
The deliciousness of the cakes with 2-shaped candles are $B_1, B_2, \ldots, B_Y$.
The deliciousness of the cakes with 3-shaped candles are $C_1, C_2, \ldots, C_Z$.

Takahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.

There are $X \times Y \times Z$ such ways to choose three cakes.

We will arrange these $X \times Y \times Z$ ways in descending order of the sum of the deliciousness of the cakes.

Print the sums of the deliciousness of the cakes for the first, second, …, $K$-th ways in this list.

【输入】

Input is given from Standard Input in the following format:

$X$ $Y$ $Z$ $K$

$A_1$ $A_2$ $A_3$ … $A_X$

$B_1$ $B_2$ $B_3$ … $B_Y$

$C_1$ $C_2$ $C_3$ … $C_Z$

【输出】

Print $K$ lines.

The $i$-th line should contain the $i$-th value stated in the problem statement.

【数据范围】

$1 \leq X, Y, Z \leq 1000$
$1 \leq K \leq \min(3000, X \times Y \times Z)$
$1 \leq A_i \leq 10,000,000,000$
$1 \leq B_i \leq 10,000,000,000$
$1 \leq C_i \leq 10,000,000,000$

【输入样例1】

【输出样例1】

For example, there are $2 \times 2 \times 2 = 8$ ways to choose three cakes, as shown below in descending order of the sum of the deliciousness of the cakes:

$(A_2, B_2, C_2): 6 + 5 + 8 = 19$
$(A_1, B_2, C_2): 4 + 5 + 8 = 17$
$(A_2, B_1, C_2): 6 + 1 + 8 = 15$
$(A_2, B_2, C_1): 6 + 5 + 3 = 14$
$(A_1, B_1, C_2): 4 + 1 + 8 = 13$
$(A_1, B_2, C_1): 4 + 5 + 3 = 12$
$(A_2, B_1, C_1): 6 + 1 + 3 = 10$
$(A_1, B_1, C_1): 4 + 1 + 3 = 8$

【输入样例2】

【输出样例2】

【输入样例3】

10 10 10 20
7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488
1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338
4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736

【输出样例3】

23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547